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WORKING PAPER · NO. 2018-74

Rebel Capacity, Intelligence Gathering, and the Timing of Combat Operations Konstantin Sonin, Jarnickae Wilson, and Austin L. WrightOCTOBER 2018

Rebel Capacity, Intelligence Gathering, and

the Timing of Combat Operations∗

Konstantin Sonin, Jarnickae Wilson, and Austin L. Wright†

October, 2018

Abstract

Classic theories of counterinsurgency claim rebel forces execute attacks in an unpre-

dictable manner to limit the government’s ability to anticipate and defend against

them. We study a model of combat and information-gathering during an irregular

insurgency. We test empirical implications of the model using newly declassified mil-

itary records from Afghanistan that include highly detailed information about rebel

attacks and counterinsurgent operations, including close air support missions, bomb

neutralizations, and covert government-led surveillance activity. Our conflict micro-

data also include previously unreleased information about insurgent-led spy networks,

where rebels monitor troop movement and military base activity, as well as military

base infiltration and insider attacks. We couple these data with granular information on

opium production and farmgate prices. Consistent with our simple theoretical model,

we find that the capacity (wealth) of local rebel units influences the timing of their at-

tacks. As rebels gather more resources, their attacks become temporally concentrated

in a manner that is distinguishable from randomized combat. This main effect is sig-

nificantly enhanced in areas where rebels have the capacity to spy on and infiltrate

military installations. Taken together, these findings suggest economic shocks that

increase the capacity of insurgents may influence the timing of rebel attacks through

the acquisition of precise information about military weaknesses.

∗For advice and comments, we thank Peter Deffebach, Francois Libois, Kyle Pizzey, Oliver Vanden Eynde,and Liam Wren-Lewis. This material is based in part upon work supported by the Pearson Institute forthe Study and Resolution of Global Conflicts. Eli Berman, Ethan Bueno de Mesquita, and Jacob Shapiroare owed a particular debt of gratitude for their support of this and related projects. Maria Ballesteros,Connie Guo, Lana Kugli, Michelle Liang, Yonatan Litwin, Paul Soltys, and Julian Waugh provided excellentresearch assistance.†Harris School of Public Policy, The University of Chicago, Chicago, IL 60637. Emails:

ksonin@uchicago.edu, jarnicaew@uchicago.edu, and austinlw@uchicago.edu.

1 Introduction

In the 21st century, intrastate conflicts have replaced interstate ones as the main source of

human loss and population displacement. Resource endowments shape how rebels recruit,

retain, and deploy their fighters (Weinstein, 2007). As insurgents accumulate capacity, they

can expand their control of strategic territory (Kalyvas, 2006). Territorial control influences

how rebels treat civilians (Wood, 2014), whether civilians cooperate with rebels or collude

with government forces (Condra and Shapiro, 2012), and impacts the ability of the govern-

ment to engage in development and reconstruction (Sexton, 2016). Rebel capacity defines

even the finest dimensions of internal warfare.

One central question that remains largely unexplored is whether rebel capacity influences

how rebels fight. In particular, classic theories of insurgency note that the rebel’s main

advantage in an asymmetric conflict is the ‘element of surprise’ (Galula, 1964). If guerrillas

aim to undermine their more powerful rivals, their attacks must be unpredictable and, as

such, difficult for government forces to anticipate and thwart (Thompson, 1966; Powell,

2007a,b). Yet the strategic value of random combat may diminish as rebels accumulate

resources. As their capacity grows, rebels may shift from guerrilla tactics to conventional

warfare, where frontal assaults are less random and more costly to the rebel forces, but enable

insurgents to consolidate territorial and economic control. Additional resources might also

allow rebels to gather precise information about defensive weaknesses, including when troops

and military installations are vulnerable to attack.

These dynamics motivate our theoretical argument. In our model of combat, rebels

allocate scarce resources to conducting attacks at various times. The government also invests

in defensive tactics to ‘harden’ (deter) against attacks at particular times when troops and

bases might otherwise be vulnerable. Once the government allocates protection, the rebels

obtain some noisy information about the protection (i.e., when targets are vulnerable). As

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government resources are scarce, information about the presence of protection at one point

in time is simultaneously information about (the absence of) protection during other periods

of the day. With higher quality information, rebels concentrate their attacks on times when

targets are unprotected. This suggests a simple theoretical mechanism linking rebel capacity

and the temporal randomness of insurgent attacks. With few resources, rebels can acquire

relatively worse information (i.e., lower quality), and attacks appear to be more randomly

timed (i.e., the timing of attacks exhibit higher entropy when the quality of information is

lower).

We test the empirical implications of our model using newly declassified military records

provided to us by the United States government. These records document hundreds of thou-

sands of combat engagements in Afghanistan during Operation Enduring Freedom, including

28,678 instances of indirect fire attacks (typically rocket or mortar fire). These data are par-

ticularly valuable because they include within-day timestamps (often to the minute), which

we collapse to the hour. This rich feature of the data allows us to study temporal clustering

in attack patterns, consistent with a deviation from random attack timing. We quantify the

randomness of combat timing by developing and implementing a novel extension of boot-

strapping methods in statistics applied to the canonical Kolmogorov-Smirnov test. This

method yields a likelihood parameter capturing the probability an empirical distribution

of combat timing can be distinguished from a random attack pattern. We then study the

association between temporal clustering and rebel capacity using granular data on opium

revenue, which the insurgents consistently tax at a fixed rate (Peters, 2009).

We find evidence that the randomness of attacks significantly decreases as rebels ac-

cumulate more resources from the opium trade. As rebels accumulate fighting capacity,

their attacks become temporally clustered around particular time windows in the day. This

core result survives a number of robustness checks, including accounting for trends in rebel

violence during the fighting, harvest, and planting seasons, which may influence the inten-

2

sity of opium cultivation from year to year. The richness of our microdata also enables us

to rule out additional concerns about the positive covariance between rebel capacity and

strategic reallocation of government forces. We do this by accounting for variation in the

location and timing of 5,410 close air support missions, 43,679 bomb neutralizations, 1,279

raids on insurgent safe houses, the capture and detention of 13,839 rebel fighters, and 776

covert government-led surveillance operations. Our military records also allow us to address

potential concerns about the role of non-lethal coercion of opium production.

The following simple example (Example 1) illustrates the basic logic of our model,

which captures a common feature of irregular warfare. Counterinsurgents deploy technology

to protect bases from attack. Troop and vehicle movement as well as day-to-day operations

make military installations more or less vulnerable during certain time slots (hours of the

day). This was the case in Uruzgan province following the Afghan surge in 2010, when insur-

gents were able to monitor and assess weaknesses at one of the Coalition’s forward operating

bases.1 Rebels had amassed an arsenal of rockets, which they deployed strategically at par-

ticular times during the day. Despite quick reaction times and a technological advantage,

Coalition forces were unable to neutralize the insurgent threat and carefully timed attacks

continued during the subsequent fighting season.

Example 1 Suppose that a rebel group considers launching attacks at two time intervals

during the day, and that the government has resources to defend against attacks during only

one period. The choice for the rebel group is whether to launch attacks at both times or

attack during one period with a double strength. If a target is protected by the government

when the attack occurs, the attack does not succeed. If the target is unprotected during the

strike, the attack’s chance of success is p, 0 < p < 1; the probabilities are i.i.d..

Suppose that the government moves first: the equilibrium strategy is to randomize be-

tween the two time periods with probability 1/2. In the absence of any information, attacks

1See https://tinyurl.com/y8e5x466.

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on different time slots result in one rebels’ success with probability p; two attacks during the

same time slot result in two successes with probability 12p2, and one success with probability

p (1− p) . Now, suppose that after the defense is allocated, the rebels gathered information

and the posterior probability that the first time window is vulnerable is q > 12. Launching

attacks at two different times results in the expected harm of p and the probability that at

least one attack is successful of p. As q > 12, if two attacks are launched, this is done in

the first time window. The expected harm is 2qp2 + 2qp (1− p) , which exceeds p for any

q > 12, and the probability that at least one attack is successful is qp2 + 2qp (1− p) , which

exceeds p as long as q > 12−p . Intuitively, rebels concentrate their rocket fire (or attacks more

generally) when the attacking technology is inefficient (p is low) and intelligence about when

the is target vulnerable is high quality (q is high).

The attacks become more temporally concentrated when information about target vul-

nerability is more precise. Now, suppose that rebels receive conditionally independent binary

signals si ∈ {V,D} such that Pr(si = V |V ) = Pr(si = D|D) = θ ≥ 12, larger θ corresponding

to a more precise information. (These signals are not independent as if the first time slot is

vulnerable, the second is not, and vice-versa.) Furthermore, suppose that s1 = V, s2 = D.

Then q = θ2

θ2+(1−θ)2 , which is increasing in θ, and a higher θ makes concentration of attacks

more likely. Thus, when rebels have fewer resources and spend less on information gath-

ering, their attacks become less concentrated. In Section 2, we analyze the equilibrium of

this model for any number of time slots N, periods that are protected by the government

disposal R, and rebel capacity (the number of possible attacks) A.2

Afghanistan provides an ideal setting to test the potential mechanisms that explain the

2The general setup might be familiar to a reader: a particular case of our model can been used todemonstrate the popular “Monty Hall paradox” (e.g., Gill, 2010). In the model with N = 3, R = 2, p = 1,A = 1, if the rebels’ choice is known to the government and it does, without reallocating the defense, revealthat one of the non-chosen periods is protected, the optimal ex ante strategy for rebels is to switch away fromtheir initially chosen time of attack. In the setup with partial information, our general case, the optimalityof switching would depend on the parameters of the model.

4

relationship between rent extraction and the timing of insurgent attacks. To do this, we first

develop a methodology for quantifying temporal clustering in our data, extending the boot-

strap Kolmogorov-Smirnov tests described by Abadie (2002). We next turn our attention to

the intelligence gathering mechanism.

In particular, our model suggests that the quality of information that insurgents can

gather about troop and facility weakness influences the level of sophistication exhibited by

the temporal patterns of combat activity. As insurgents gather enough sufficiently precise

information about target vulnerabilities, their attack patterns will shift as they optimally

calibrate the timing of their attacks. Our military records include previously unreleased

information about rebel spy operations (surveillance of troop movement and base activity)

observed by military forces. Our data suggests that insurgents were able to conduct surveil-

lance operations in 70 of Afghanistan’s 398 districts in 2006 (see Figure 6). These records

also include data on security breaches, which occur when insurgents are able to effectively

infiltrate the outer perimeter of targets and observe activity from within bases and outposts.

Finally, consistent with these measures, we track incidents where the Taliban are able to

‘turn’ security recruits and use them to launch demoralizing attacks within army units. In

2006, insurgents were able to infiltrate bases in four districts and conduct insider attacks in

five. These data yield a unique opportunity to test whether the ability to surveil, breach, or

infiltrate targets—all of which are consistent with the capacity to acquire precise informa-

tion about target weaknesses—significantly enhances the overall impact of revenue shocks.

We find strong evidence that the baseline effect we observe is substantially greater in areas

where the Taliban have the capability to acquire actionable intelligence about when troops,

convoys, and bases are susceptible to attack.

Quantitative work on the economics of conflict has largely focused on the conditions that

trigger warfare. Fearon and Laitin (2003), Collier and Hoeffler (2004), Miguel et al. (2004),

and Bazzi and Blattman (2014) study the proximate causes of conflict. Other work explores

5

incentives to use violence as a means to predate or capture economic resources (Le Billon,

2001; Ross, 2004; Hidalgo et al., 2010). Still others have focused on the link between income

shocks and levels of political violence at a subnational level (Dube and Vargas, 2013b; Jia,

2014; Oliver, 2018). A meaningful gap exists, as Berman and Matanock (2015) point out,

between our understanding of when and how rebels engage in armed combat. We advance

this agenda by examining the relationship between economic shocks to rebel capacity and

the ways in which insurgents fight.

Violence is economically and politically costly. Gould and Klor (2010) find that ter-

ror attacks harden in-group biases and cause Israelis to adopt less accommodating political

positions.3 Those affected by these attacks are also more likely to vote for right-wing par-

ties. Similarly, Condra et al. (forthcoming) find that insurgent attacks around elections in

Afghanistan are calibrated to avoid civilian casualties and substantially reduce voter turnout.

Violence may be triggered by and reinforce ethnic divisions (Esteban and Ray, 2011; Este-

ban et al., 2012), even in institutions designed to maintain impartiality (Shayo and Zussman,

2017). Civil conflict is also economically disruptive (Abadie and Gardeazabal, 2003), even

at the microlevel (Besley and Mueller, 2012). Our results help us better understand how in-

surgents respond to rent shocks and may enable governments to more anticipate and defend

against attacks.

More generally, our model helps unpack core features of the political economy of insur-

gency. State capacity is central to economic theories of conflict (Besley and Persson, 2011;

Gennaioli and Voth, 2015; Besley and Persson, 2010; Powell, 2013; Carter, 2015; Esteban

et al., 2015). Yet the resources available to the state’s competitors also influence when con-

flicts emerge, how internal wars are fought, and whether they end in withdrawal. Recognizing

this gap, Bueno de Mesquita (2013) theorizes that the relative strength of the rebellion in-

fluences leaders’ choice to adopt irregular tactics. We advance this literature by developing

3See also Berrebi and Klor (2008) and Getmansky and Zeitzoff (2014).

6

a microlevel theory of the relationship between combat tactics and resource endowments.

Technology of conflict has long been an active area of theoretical modelling (Kress, 2012).

Optimal allocation of attacking and defensive resources have been studied in the Colonel

Blotto-type games starting with Borel (1953). (See Golman and Page (2009), Roberson and

Kvasov (2012) and Konrad and Kovenock (2009) for recent advances and Kovenock and

Roberson (2012) for an excellent survey). Our baseline model is very simple: the rebels

maximize the expected number of successful attacks. The advantage is its tractability: it

allows to add the possibility of one-sided information-gathering and comparative statics with

respect to the quality of information.

In a setting in which the maximand is the sum of harm to individual sites, Powell (2007a)

demonstrates that in the unique equilibrium, the defender minimaxes the attacker regardless

of whether or not the attacker can observe the defender’s allocation before choosing where to

launch the attack. In Powell (2007a), the defense has private information about the relative

vulnerability of two sites, and allocated protection is public information, which creates the

secrecy vs. vulnerability trade off. Goyal and Vigier (2014) consider a zero-sum Tullock-type

conflict, in which the defense chooses a network to protect and the attacker chooses where

to launch an attack. In particular, they show that a star network with all defence resources

allocated to the central node is optimal in many circumstances. In Konig et al. (2017),

the network is given; the data on the Second Congo War is used to estimate the impact of

selective dismantling of fighting groups and weapons embargoes on conflict intensity.

The rest of the paper is organized as follows. Section 2 introduces our theoretical model.

Section 3 details the empirical strategy. Section 4 presents the main results and robustness

checks. The final section concludes.

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2 Theory

In this section, we present a model that has a rebel group choosing the number of attacks

and the precision of information that they use in launching them. This is a simplest possible

model consistent with our empirical approach that utilizes randomization inference and the

bootstrap Kolmogorov-Smirnov method developed by Abadie (2002).

2.1 Setup

Consider a rebel group that attacks the government facilities using a certain technology (e.g.,

mortars). The group chooses the number of attacks A, a positive integer, and the quality of

information θ ∈ [0, 1], on which the allocation of attacks is based. The government allocates

resources to defeat attacks.

We assume that there are N time slots to protect.4 The government has resources to

defend R < N time slots . Formally, the government strategy is a function g : R→ ∆N that

maps each of R units of government’s defense into probability distribution over N time slots;

∆N denotes the standard N − 1-dimensional simplex, the set of all probability distributions

over N time slots.

If an attack happens occur during the period when a target is defended, it does not

succeed; if an attack is during unprotected time slot, it succeeds with probability p. Since any

deterministic choice of protection will result in rebels attacking outside of the time slots when

targets are defended, any reasonable placement of protection should be probabilistic. After

the government allocates protection, rebels gather intelligence about which time slots are

vulnerable. Specifically, rebels receive noisy signals (si)i∈N ∈ {V,D}N that are determined

according to Pr(si = P |P ) = Pr(si = D|D) = θ. Then the rebels strategy is a function

4It is trivial to point out that attacks are time-space objects. Here, to make the problem theoreticallyand empirically tractable, we focus on a single dimension: the timing of rebel attacks.

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a∗ : A× {V,D}N → ∆N that maps signals about periods’ vulnerability into probabilities of

attacks across each of the N time slots.

The rebel group maximizes the expected number successful attacks net of the cost of

attacks and information gathering. We assume that the marginal costs of attacks and in-

formation precision are MCA(A) = cAA and MCI = cIθ, respectively. (This assumption

grossly simplifies comparative statics - see Proposition 3; the qualitative results go through

for any cost function with increasing marginal costs.) Periods of low rents correspond to

higher marginal costs: while we do not model alternative uses of money by rebels explicitly,

this is a realistic assumption (e.g., Dube and Vargas (2013a)). The government is interested

in minimizing the expected number of successful attacks.

Timing

1. Rebels choose the number of attacks A and precision of information θ.

2. The government chooses allocation of resources across N time slots.

3. Rebels receive information (si)i∈N ∈ {D, V }N and choose attack times in AN .

4. Pay-offs are received.

Definition 1 An equilibrium is rebels’ choice of number of attacks A∗, the quality of infor-

mation θ∗, a function a∗ : A × {V,D}N → ∆N that maps signals about all times during

which attacks could occur into probabilities of attacks on each of the N time slots, and a

function g∗ : R → ∆N that maps R units of government’s defense on N time slots. Given

g∗, (A∗, θ∗, a∗) maximize the probability of a successful attack; given (A∗, θ∗, a∗), g∗ minimizes

this probability.

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2.2 The Attack Timing Game

We start backwards. Suppose that rebels have chosen the number of attacks A they launch

and precision of information θ. Our first goal is to describe a unique (symmetric) equilibrium

of the resulting subgame.

It is straightforward to establish that the government allocates resources into R protec-

tion intervals chosen randomly and uniformly across all possible combinations. The rebels’

optimal strategy depends on the signals that they observe. Information gathering results in

x “vulnerable” (si = V ) and N − x “defended” (si = D) time slots. Let q(x) denote the

ex post probability that time i with si = V is vulnerable. Importantly, although signals are

conditionally independent, a signal about vulnerability of one period is informative about

the vulnerability of other periods. Indeed, if one time slot is more likely to be vulnerable,

other time slots are less likely to be vulnerable as probability of being one of R−1 protected

time slots among N−1 periods is smaller than to be one of R among N. It is possible that the

number of “positive” (vulnerable) signals x is not equal to A; x can be any integer between

0 and N with a non-zero probability. In the two extreme cases, x = 0 (there are no time

slots that are more likely to be vulnerable) and x = N (signals suggest that all potential

times an attack could occur are equally vulnerable), there is no information to update upon.

In all other cases, 1 ≤ x ≤ N − 1, signals are informative:

P (V |si = V ) > P (V |si = D).

The number of “vulnerable” signals is a random variable, the sum of two binomial dis-

tributions with different probabilities of success: N −G vulnerable time slots produce signal

V with probability θ, while G defended time slots produce signal V with probability 1− θ.5

5The probability distribution of a sum of two or more binomial random variables, i.e. sums of independentBernoulli trials, with different success probabilities is sometimes called Poisson binomial distribution (Hillionand Johnson, 2017).

10

Proposition 1 There exists a unique equilibrium in the attack timing game, in which the

government protects R time slots chosen randomly and uniformly across all possible com-

binations and rebels follow the signals that they receive. If A ≤ x = # {si = V } , then A

attacks are distributed uniformly over x vulnerable time slots. If A > x, there is an optimal

number of attacks a(x) against a vulnerable period of time such that min {A, xa(x)} attacks

are distributed uniformly over x vulnerable time slots. The remaining A − min {A, xa(x)}

attacks are distributed uniformly across N − x time slots that are marked “defended”.

Critically, with time slots labeled “vulnerable” and “defended” after the informative

signals are received, the rebels’ optimal strategy is a function of the probability q(x) that

a given time period deemed vulnerable is indeed vulnerable. (With fixed N and R, the

probability that the time slot labeled defended is vulnerable is a function of q(x).) The

intuition is as follows. Consider the rebels’ choice of one attack across two time slots with

probabilities of being vulnerable q1 and q2, respectively, with q1 > q2. If there are no attacks

already planned on during these times, then an attack timed during the first period provides

a higher marginal probability of success.

The fact that the vulnerable time slot has a higher probability of success does not mean

that all attacks should be concentrated during times when targets are vulnerable. Suppose

that there are already m attacks planned during the first time period, m ≥ 1, and no attacks

planned on the second time slot. One more attack during the first time slot results in

q1 (1− p)m of marginal probability of success as with probability 1− (1− p)m one of the m

attacks that are already planned succeeds. An attack that occurs during the second time

window contributes q2p. This explains why, given some sufficient capacity, rebels will launch

some attacks launched during the second, less likely to be vulnerable, period regardless of

the initial distribution of probabilities q1 and q2.6

6Note that it never makes sense to “divide” attacks. The reason is that a marginal increase in x,the “share” of the second attack launched at time window 2, does not affect the marginal probability of

11

The term min {A, xa(x)} appears in the statement of Proposition 1 because it is possible

that the threshold a(x) is such that xa(x), the desired number of attacks during vulnerable

time slots, does not exceed the capacity A. For example, if N = 5, A = 3, and intelligence

about defensive weaknesses suggests two specific time windows are likely to be vulnerable,

the optimal strategy might call for m(2) = 2, i.e. two attacks should be launched during

each of the two vulnerable time slots. With the capacity of launching only three attacks,

the rebels would have to choose the period for the double attack randomly over the two

vulnerable time windows.

2.3 The Rebel’s Demand for Precise Information

The rebels’ equilibrium strategy described in Proposition 1 depends on the quality of infor-

mation θ. In the simple environment of Example 1, we demonstrated that a higher precision

of information leads to a higher temporal concentration of attacks: more attacks are launched

during time periods that intelligence gathering indicated as ”vulnerable”. This result ex-

tends to the general setup: with more precise information, for any number of “vulnerable”

signals x, the optimal strategy requires to launch more attacks during the vulnerable time

windows.

Proposition 2 For any number of attacks A, the higher is the precision of information that

rebels receive, θ, the higher is the temporal clustering (concentration) of attacks: the lower

success of this attack. Consider the following strategy by rebels in the case when when information receiveddifferentiates between the two time periods, so the posterior probability that the first time slot is protectedis q and that the second window is protected is 1 − q with q > 1

2 . Suppose that one attack is launchedduring time window 1, and let x denote the probability that the other attack is launched during time slot 1as well. Then the case of “two attacks during time slot 1” corresponds to x = 1, and “attack during eachtime period” corresponds to x = 0, but the strategy allows for a more general distribution of attacks. Theprobability that at least one attack is successful is given by

q(x(p2 + 2p (1− p)

)+ (1− x) p

)+ (1− q) (1− x) p,

which is a linear function in x. Generically, the optimal choice is either to launch two attacks during a giventime window 1 (when q > 1

2−p ), or to attack during each of the two periods, but never to “mix”.

12

is the expected number of unique periods attacked and the larger is the expected number of

attacks (both successful and total) per time slot attacked.

The critical element of Proposition 2 is that for any number x of time slots that are

considered vulnerable after the information is collected, the probability q(x) that a time

window marked vulnerable is indeed vulnerable is (weakly) increasing in the precision of

information θ, and thus the threshold a(x) is (weakly) increasing in θ for any x. As a

consequence, more precise information leads to a higher concentration of attacks: more

attacks are launched during a smaller number of unique periods (of the day).

In the extreme case of perfect information (θ = 1), attacks are randomized over all

vulnerable times during which an attack could be launched. In the opposite extreme, when

the signals are not informative at al (θ = 12), all time windows are equally likely to be

vulnerable. In this case, the optimal strategy for rebels is to launch A attacks during

different times chosen randomly and uniformly across all possible choices guaranteeing that

two attacks are not launched during the same time window (unless, of course, A > N).

2.4 The Optimal Timing of Attacks

Now that we have determined the relationship between the precision of information that

rebels receive and the temporal concentration of their attacks for any fixed number of attacks,

we can analyze the choice between harvesting information and launching more attacks in the

main game.

In the equilibrium, the optimal choice of rebels are functions of the marginal costs of an

attacks cA and information precision cI , the number of potential time slots for attacks N, the

resources in the disposal of the government R, and the efficiency of weapons p. Naturally,

when the cost of an attack for rebels increases, they cut down on both the number of

attacks and the precision of information that they use. As a result, their attacks become

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less concentrated during particular periods of the day: when rebels are relatively weak (i.e.,

revenue-poor), their attacks become increasingly random w.r.t. timing. (In the extreme case

of no information, the maximum entropy of attacks is achieved as rebels use the uniform

distribution of attacks over all possible time slots.) This increase in entropy, which is the

main concept in the statistical method developed in Abadie (2002), as a result of decrease

in resources is the central empirical implication of our model which tests in the next section.

The increase in government resources has the same effect, but for a different reason. A

higher R decreases the probability of rebels’ success as the ex ante probability that each time

window is protected increases. Consequently, rebels spend less on information gathering and,

in equilibrium, their attacks become less temporally concentrated. Proposition 3 formally

states the comparative statics results.

Proposition 3 There exists a (subgame perfect) equilibrium of the game, in which the rebels

optimally choose the number of attacks and the quality of information that they gather before

the attack timing game.

(i) A higher marginal cost of information, cI , or a higher marginal cost of an individual

attack, cA, results in the lower optimal precision of information, θ∗. Consequently, the rebels’

attacks become more randomly timed (i.e., less concentrated): a smaller share of total number

of attacks are launched during the same time windows.

(ii) More resources in the government’s disposal, R, and less efficient weapons (lower

p) result in lower demand for information, and, therefore, lower temporal concentration of

attacks.

3 Empirical Design

In this section, we discuss the setting of our investigation, review our microdata, and intro-

duce our identification strategy.

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3.1 Context

We study the relationship between combat activity and rebel capacity in Afghanistan. We

focus specifically on the well-documented link between opium production and Taliban tax

extraction. In the primary opium producing regions, seeds are planted in late fall and early

winter. The growing season ranges from February through April, with most opium latex

harvested and packaged in May and June. Taliban commanders and veteran fighters return

from Pakistan in June to collect taxes from opium farmers (ushr, typically a flat 10% fee

mandated by the Quran).7 Taxes can be paid in currency, opium blocks, or other goods, such

as motorcycles, offroad vehicles, and weaponry. The Taliban also benefits from protection

fees levied on opium traffickers as they pass through rebel-held territories.

Taxes are collected by fighters and receipts are distributed to farmers to prevent double

taxation. Fighters pass their collections to district-level commanders (equivalent in scale to

US counties). Taxes are subsequently passed upward to provincial and regional commanders,

who keep ledgers of their annual revenue and are subject to audit by the Taliban’s Central

Finance Committee, based out of southwestern Pakistan. Most proceeds remain with the

district commander, for conducting operations in the subsequent fighting season which typi-

cally lasts until September. These funds can be used to purchase weapons and ammunition,

as well as covering the salaries of fighters and rebel informants. The Central Finance Com-

mittee retains the authority to demote or relocate field commanders to less desirable fronts if

audit irregularities are found. The remaining revenue is split between supporting operations

conducted in resource-poor districts where local taxes alone are insufficient for supporting

rebel attacks and developing Taliban infrastructure in Pakistan (including small-scale hos-

pitals for wounded fighters).

We focus primarily on the period from 2006 to 2014. The industrial organization of the

7For a detailed account of the industrial organization of the Taliban, see Peters (2009).

15

insurgency, most notably the taxation and command structures oriented around administra-

tive districts, emerged in 2006. Our military records track insurgent operations until the end

of 2014, when the NATO Operation Enduring Freedom was transitioned to Mission Resolute

Support.

3.2 Conflict Microdata

Our investigation exploits newly declassified military records which catalogue combat engage-

ments and counterinsurgent operations during Operation Enduring Freedom in Afghanistan.

These data were maintained by and retrieved through proper declassification channels from

the U.S. Department of Defense. The data platform was populated using highly detailed

combat reports logged by NATO-affiliated troops as well as host nation forces (Afghan mili-

tary and police forces). Data of this type differ substantially in coverage and precision from

media-based collection efforts (Weidmann, 2016). As Weidmann (2016) points out, these

tactical reports represent the most complete record of the war in Afghanistan. Additional

details on data collection are discussed in Shaver and Wright (2017).

The detailed nature of our conflict microdata allows us to track insurgent activity by

the hour. Although this data tracks dozens of types of violence, the majority of enemy

action events are characterized as indirect fire, direct fire, and IED explosions. Indirect

fire consists of mortars and other weapons that can be deployed without close contact with

military forces. Direct fire attacks are primarily line-of-sight, close combat events. IEDs

consist of explosives that have been emplaced and are detonated through a variety of trigger

mechanisms (pressure plate, cable-to-battery, radio signal, laser beam, etc.). Subsets of

these data are also studied in Callen et al. (2014), Beath et al. (2013), and Condra et al.

(forthcoming), and are highly comparable to tactical data collected in Iraq Berman et al.

(2011).

It is important to note that insurgents have differential control over the exact timing

16

of each of these types of combat. Indirect fire events can be initiated at any time against

stationary targets. For example, a large number of mortar fire attacks were launched from

hillsides and targeted military outposts. As such, insurgents maintained a high level of

control over when these evente occurred. Direct fire attacks are typically frontal assaults

on convoys or forward deployed troops conducting combing operations in remote villages.

Although insurgents decide if to attack, conditional on having the opportunity, the timing of

these attacks is partially determined by the movement of troops, the timing of which may be

determined by a non-stochastic process. Similarly, roadside bombs may be planted hours or

days before they are triggered. Some of these bombs may also be detonated by unintended

targets, which further reduces insurgent control over the timing of these attacks. For these

reasons, we focus our main analysis exclusively on the timing of indirect fire attacks.

Our military records include information about counterinsurgent operations, including

find and clear missions that neutralized emplaced IEDs, discoveries of weapon caches, such

as small arms, ammunition, and bomb making materials, and provision of close air sup-

port, which was used primarily to harden mobile targets and extract coalition forces that

were pinned down at a fixed location by insurgents. We supplement this information with

measures of insurgent capture and detention, counterinsurgent surveillance operations, and

safe house raids yielding actionable intelligence about rebel operations. This information

enables to address operational factors that may confound the relationship we are trying

to estimate. In particular, it might be the case that counterinsurgents strategically assign

additional fighting capacity to districts with a substantial rebel presence and where opium

production is high. Shifts in government resources, like the ability to identify and neutralize

weapon caches or to use aerial bombardment to assist troops engaged by insurgents, might

also influence the temporal patterns of insurgent attacks.

It is also possible that opium production is influenced not just be combat operations,

but also more direct attempts by insurgents to coerce the local population. In particular,

17

insurgents may use violent and non-violent tactics to intimidate civilians, such as killings

of government collaborators and the posting of ‘night letters’ and other non-lethal shows

of force. Fortunately, our military records include information about these tactics as well,

enabling us to address potential concerns about residual endogeneity in estimated levels of

opium production.

Another unique feature of our conflict data is information on rebel surveillance opera-

tions, military installation breaches, and insider attacks. Enemy surveillance operations are

logged whenever security forces become aware of attempts by insurgents to track troop and

vehicle movement and day-to-day activities on military bases. This kind of insurgent spy

activity can be, and likely is, used to identify troop and infrastructure vulnerabilities. We

illustrate the location of these spy operations in Figure 6. In addition to surveying force

activity from outside of military compounds, insurgents can infiltrate these installations and

monitor activity from within. These security breaches might also result in direct confronta-

tions between insurgent and counterinsurgent forces. Records of insider attacks also reveal

Taliban attempts to ‘turn’ Afghan security forces, and launch deadly attacks from within

operational units. We use these incredibly unique pieces of information to more explicitly

test the observable implications of our model regarding intelligence gathering and the quality

(precision) of information about government vulnerabilities.

3.3 Opium Cultivation and Prices

We supplement our military records with data on opium production and prices. Opium

production estimates are derived from ground-validated remote sensing techniques, which

use high resolution satellite imagery to track changes in vegetation during the spring har-

vest. UNODC-Afghanistan randomly spatially samples potential agricultural zones within

provinces and acquires pre-harvest and post-harvest imagery (see Figure 2, panel (a)). These

images are then examined for changes in vegetative signatures consistent with the volatile

18

Figure 1: Military records indicate the location of rebel surveillance operations conductedin Afghanistan (2006).

Notes: Data on insurgent spy operations drawn from SIGACTS military records. Cross hatch patternindicates insurgents conducted at least one detected surveillance operations during 2006, the first year of oursample. District boundaries are drawn from the ESOC Afghanistan map (398 districts).

wetness of opium plants after lancing. From this sampling technique, officers estimate the

spatial risk of opium production. This enables them to calculate granular estimates of opium

production (see Figure 2, panel (b)). These gridded estimates are then compiled as the an-

nual amount of opium production (in hectares) for each district. We correct for changes in

the administrative boundaries of districts over time using the Empirical Studies of Conflict

(ESOC) administrative shapefile. To translate production into yields, we compile additional

details about annual yield (kilograms per hectare) from UNODC-Afghanistan annual reports.

These figures are available at the national level as well as by region.

Opium price data is compiled at national and regional levels. These prices are tracked

monthly at various locations across the country via a farmer and market spot price survey

19

system. In Figure 2, panel (a), we introduce the monthly time series for the two price-

making regions, Kandahar and Nangahar. Our main specification utilizes the simple average

between these prices in June, when taxes are collected (vertical lines added for clarity). In

supplemental results, we study the regional price time series in Figure 2, panel (b). We rely

on UNODC-Afghanistan documentation to assign districts to price zones. We extract exact

prices using WebPlotDigitzer software.

Figure 2: UNODC Methodology for Estimating Annual District Drug Production.

(a) Sampling Satellite Imagery (b) Impute Production from Imagery/Field Obs.

Notes: Methodological figures and details drawn from the 2016 UNODC-Afghanistan Drug Report. Panel(a) demonstrates the sampling design used when acquiring high resolution satellite imagery (location: Kan-dahar). Panel (b) illustrates the subsequent production estimation, which combines low and high resolutionimagery (location: Nangahar).

3.4 Detecting Random Timing of Combat

We now introduce a method for detecting the randomness of attack timing. Our approach

employs randomization inference and the bootstrap Kolmogorov-Smirnov method developed

by Abadie (2002). The method is executed in several steps.

1. Fit a local polynomial regression to the observed distribution of violence by hour. We

specify a conservative bandwidth of 1. This empirical distribution of fitted values is

20

Figure 3: Time series data on opium prices collected at national (a) and regional (b) levels.

(a) National price TS (b) Regional prices TS

Notes: Figures on national and regional price time series drawn from the 2016 UNODC-Afghanistan DrugReport. Underlying data compiled from farmer and market spot price surveys conducted throughout theyear. In Panel (a), the simple average is calculated (Nangahar, Kandahar). In Panel (b), we assign districtsto regions according the UNODC documentation. Prices were precisely extracted using WebPlotDigitzer.

stored.8

2. Identify the sequence of district-hours during which indirect fire engagements occur.

For each district-hour, we know the sum of the number of attacks.

3. Randomly shuffle the sequence above. This is equivalent to a randomization or per-

mutation test.

4. Fit a local polynomial regression to the randomly shuffled distribution of violence by

hour. The simulated distribution of fitted values is stored.

5. Execute the bootstrap Kolmogorov-Smirnov test. This test is composed of four ele-

ments.

(a) Compute the TKSdfi for the fitted values of the empirical and simulated distribu-

tions, where:

8Some conflict events lack a time stamp (∼3%). Because we cannot assign these events an hour, they areexcluded from the calculation of the empirical distribution.

21

TKSdfi =

(n1n0

n

) 12

supy∈R∣∣F1,n1(y)− F0,n1(y)

∣∣.(b) Resample observations with replacement from observed and simulated distribu-

tions. Split the resampled set into two distributions and calculate TKSdfi,b. Store

TKSdfi,b.

(c) Repeat prior two steps 1,000 times.

(d) Calculate and store the likelihood parameter of the tests as∑1000

b=1

1TKSdfi,b>T

KSdfi

1,000.

6. Repeat steps 2 through 5 10,000 times. Evaluate the central tendency (mean) of the

likelihood parameters.

7. Replace zero values with the minimum observed non-zero rank value and calculate the

log.

To clarify, we identify the hour of each attack within a given district-year (fighting season).

We then reshuffle the hour vector and compare the empirical distribution to the randomly

reshuffled vector. This process is repeated many times per district-year. The result of

the technique is a single likelihood parameter, which we call a p-value, for each unit of

observation. We estimate these parameters for district-years with a minimum of five conflict

events.9 Higher p-values indicate that the distribution of rebel attacks by hour cannot be

distinguished from randomness. Lower p-values reveal attack patterns that are more easily

differentiated from randomness; i.e., they are more predictable.

Estimation of our likelihood parameters using this technique requires tens of billions of

simulations, so we use several supercomputers. In Figure 4, we plot the the calculated p-

value (log) distribution for indirect fire attacks. Most district-year p-values above -10. This

9We set the lower threshold at five events to ensure convergence of the simulations. A conflict vector thatis too short (i.e., fewer than five) does not permit sufficient randomization when the hour vector is reshuffled.Our results are highly consistent if we raise this threshold upward.

22

distribution is characterized by a long left-side tail. This suggests that specific district-

fighting seasons exhibit very clear evidence of temporal clustering (i.e., non-randomness).

Figure 4: Distribution of p-values from randomization test of combat in Afghanistan

0

.1

.2

.3

Den

sity

of p

-val

ues

-25 -20 -15 -10 -5 0Logarithm of p-values from KS test -- Indirect Fire Attacks

3.5 Empirical Strategy

We study the relationship between rebel capacity and randomized combat by examining

whether the within-day distribution of violence for each district’s fighting season is associated

with rent extraction from opium. If the results follow our expectations, rebel capacity and

the likelihood parameter of our simulation test above should be negatively correlated.

To test the relationship between randomization of attack timing and insurgent capacity,

we estimate the following ordinary least squares regression:

log(pvald,y) = α + β1log(productiond,y + 1)× log(pricey) + β2Xy + ΛXVd,y + ε (1)

Where pvald,y is the p-value for a given district, d, and fighting season ,y (year). Xy

captures fighting season fixed effects and XVd,y captures a vector of additional covariates,

which we incorporate to address potential concerns about omitted variables. These covariates

23

include the intensive margin of insurgent operations during the fighting, harvest, and planting

seasons as well as supplemental measures of state capacity and insurgent intimidation. We

expect the first coefficient β1 to be negative.

4 Results

We begin by visualizing the data. In Figure 5, we plot the p-value distributions for indirect

fire attacks against the corresponding opium revenue of each district-year (fighting season).

Confidence regions (95%) are shaded in blue. Notice the consistently negative relationship

between revenue and randomness of combat. This non-parametric correlation is consistent

with our intuition that high capacity rebels produce patterns of violence that are less random

and exhibit temporal clustering.

Figure 5: Bivariate relationship between opium revenue and p-value of randomization testof combat (indirect fire attacks) in Afghanistan

0

20

40

60

80

100

Opi

um re

venu

e

-25 -20 -15 -10 -5 0Logarithm of p-values from KS test -- Indirect Fire Attacks

Observed opium revenue/p-value Fit line with 95% CI

We next turn to our regression-based evidence. In Table 1, we estimate equation 1.

Column 1 is a sparse model that demeans our bivariate correlation by fighting season. We

24

find that a strong negative relationship between opium revenue and combat randomness,

confirming our visual evidence. In Columns 2 through 4 we sequentially add controls for

the intensive margin of fighting during the fighting, harvest, and planting seasons respec-

tively. We do this to address potential concerns that our bivariate result is driven by a

strong relationship between opium revenue and the intensity of violence during the fighting

season (which covaries negatively with our randomness parameter). Our results are largely

unaffected, although our point estimate becomes marginally more precise in Column 2. In

Column 3, we attempt to rule out concerns that our estimates are substantially biased by

the endogenous relationship between opium production and insurgent violence during the

harvest season, which might influence subsequent conflict during the later fighting months.

It might also be the case that farmers are coerced into planting opium through violence ex-

posure. We account for this potential source of bias by including a planting season violence

trend in Column 4. This baseline evidence suggests a precise, consistent link between rebel

capacity and randomization of indirect fire attacks.

Table 1: Impact of rebel capacity on within-day randomization of indirect fire attacks

Opium Revenue -0.0581∗∗∗ -0.0588∗∗∗ -0.0549∗∗∗ -0.0549∗∗∗

(0.0137) (0.0135) (0.0125) (0.0125)

Model ParametersFighting Season FE Yes Yes Yes YesFS Trend Yes Yes YesPS Trend Yes YesPLS Trend YesModel StatisticsNo. of Observations 600 600 600 600No. of Clusters 154 154 154 154R2 0.154 0.171 0.187 0.187

Notes: Outcome of interest is the (log) p-value of the randomness test.The quantity of interest is opium revenue for a given district-year. All re-gressions include fighting season fixed effects. Column 2-4 add controls forthe intensive margin of fighting during the fighting, harvest, and plantingseasons respectively. Heteroskedasticity robust standard errors clusteredby district are reported in parentheses. Stars indicate *** p < 0.01, **p < 0.05, * p < 0.1.

25

We conduct several other baseline robustness checks in Table 2. In Column 1, we intro-

duce a province×year fixed effect, which soaks up any residual mechanism design effects due

the spatial sampling procedure utilized by the UNODC to estimate local opium production.

This fixed effect also absorbs troop rotation schedules which coincide with the province-year,

which includes force movement into and out of regional command posts. Although the mag-

nitude and precision of our main effect declines marginally, the negative relationship persists

even in this very demanding specification. Another potential concern one might have is that

the strategy we use to account for the intensive margin of violence during the fighting season

(i.e., partialling out the violence in levels) is incomplete. Another solution is to inversely

weight our model along this margin. This implies that our corresponding estimate is less

vulnerable to vertical (conflict) outliers. We present this result in Column 2, which is highly

consistent with our baseline result.

In our baseline specification, we rely on a national time series in prices and year-by-year

variation in opium yields (kilograms per hectare). Yet the interaction of weather conditions

and soil suitability may lead to heterogeneous crop yields by region and year. Regional prices

might also differ substantially. These two concerns represent classical error-in-variables,

which we can correct with regional price and yield data compiled from UNODC records.

We replicate our baseline specification in Column 3 using opium revenues calculated using

regional yield rates and regional price data. It is also the case that some provinces have

later harvests which occur after fighting has begun in other parts of the country. We use

crop calendar maps produced by the UNODC to classify late harvest districts and exclude

them from our sample in Column 4. Again, our results are highly consistent in both model

specifications.

4.1 Threats to Inference

In this subsection we detail additional potential threats to inference.

26

Table 2: Impact of rebel capacity on within-day randomization of indirect fire attacks,robustness checks

Opium Revenue -0.0450∗∗ -0.0531∗∗∗ -0.0543∗∗∗

(0.0220) (0.0116) (0.0126)Opium Revenue (Regional) -0.0555∗∗∗

(0.0128)

Model StatisticsFighting Season FE Yes Yes Yes YesFS Trend Yes Yes Yes YesPS Trend Yes Yes Yes YesPLS Trend Yes Yes Yes YesProv×Year FE YesIM Weighted LS YesRegional Yield Adjust. YesEarly Harvest Only YesModel StatisticsNo. of Observations 600 600 600 588No. of Clusters 154 154 154 150R2 0.379 0.188 0.184 0.184

Notes: Outcome of interest is the (log) p-value of the randomness test. Thequantity of interest is opium revenue for a given district-year. All regressionsinclude fighting season fixed effects as well as controls for the intensive mar-gin of fighting during the fighting, harvest, and planting seasons respectively.Additional parameters are noted in the table footer. Heteroskedasticity ro-bust standard errors clustered by district are reported in parentheses. Starsindicate *** p < 0.01, ** p < 0.05, * p < 0.1.

It is possible that revenue from opium production may attract additional counterinsurgent

investments. Consistent with our theoretical model, to defeat rebels accumulating resources,

security forces may have deployed additional resources that could complicate estimation

of the effect of rebel capacity on the randomness of combat. We focus on six measures of

counterinsurgent capacity: close air support missions, cache discoveries, IED neutralizations,

detention of insurgent forces, counterinsurgent surveillance operations, and safe house raids

yielding actionable intelligence assets (salary and recruitment logs, hard drives, forensic

materials, etc.). We sequentially add these covariates to equation 1. We present these

results in Tables 3 and 4. For comparison, the most conservative specification from Table

1 (Column 4) is included as Column 1 in both of these tables. Notice that these measures

of counterinsurgent capacity improve the explanatory power of our models, although the

27

magnitude of the main effect is slightly attenuated.

Table 3: Impact of rebel capacity on within-day randomization of indirect fire attacks,accounting for state capacity measures (part i)

Opium Revenue -0.0549∗∗∗ -0.0336∗∗∗ -0.0418∗∗∗ -0.0276∗∗∗

(0.0125) (0.00779) (0.0106) (0.00965)

Model StatisticsFighting Season FE Yes Yes Yes YesFS Trend Yes Yes Yes YesPS Trend Yes Yes Yes YesPLS Trend Yes Yes Yes YesClose Air Support YesWeapon Caches FC YesIEDs FC YesModel StatisticsModel StatisticsNo. of Observations 600 600 600 600No. of Clusters 154 154 154 154R2 0.187 0.337 0.242 0.310

Notes: Outcome of interest is the (log) p-value of the randomness test. Thequantity of interest is opium revenue for a given district-year. All regres-sions include fighting season fixed effects as well as controls for the inten-sive margin of fighting during the fighting, harvest, and planting seasonsrespectively. Additional parameters are noted in the table footer. Het-eroskedasticity robust standard errors clustered by district are reported inparentheses. Stars indicate *** p < 0.01, ** p < 0.05, * p < 0.1.

Opium production might also be influenced by coercive tactics used by the Taliban to

intimidate civilians. In general, these tactics are difficult to track. These coercive tactics

represent a problematic omitted variable if they are indeed correlated with production and

further correlated with the sophistication of combat tactics used during the fighting sea-

son. These are plausible concerns. To address them, we incorporate additional information

from our military records which tracks attempts to intimidate the civilian population, using

methods like ‘night letters’ and shows of non-lethal force as well as deliberate killings of

government collaborators (like informants and security force recruits). Our main effect is

only slightly attenuated when we account for these rebel intimidation tactics in Columns 2

and 3 of Table 5.

28

Table 4: Impact of rebel capacity on within-day randomization of indirect fire attacks,accounting for state capacity measures (part ii)

Opium Revenue -0.0549∗∗∗ -0.0454∗∗∗ -0.0548∗∗∗ -0.0484∗∗∗

(0.0125) (0.0104) (0.0123) (0.0113)

Model StatisticsFighting Season FE Yes Yes Yes YesFS Trend Yes Yes Yes YesPS Trend Yes Yes Yes YesPLS Trend Yes Yes Yes YesInsurgent Detention YesCOIN spies YesSafe house raids YesModel StatisticsNo. of Observations 600 600 600 600No. of Clusters 154 154 154 154R2 0.187 0.249 0.187 0.217

Notes: Outcome of interest is the (log) p-value of the randomness test. Thequantity of interest is opium revenue for a given district-year. All regressionsinclude fighting season fixed effects as well as controls for the intensive mar-gin of fighting during the fighting, harvest, and planting seasons respectively.Additional parameters are noted in the table footer. Heteroskedasticity ro-bust standard errors clustered by district are reported in parentheses. Starsindicate *** p < 0.01, ** p < 0.05, * p < 0.1.

4.2 Mechanisms: Heterogeneous Effects of Intelligence Gathering

Having addressed numerous potential threats to inference, we now turn our attention to a

more direct test of our model’s empirical implications. Our results could be working through

at least two plausible mechanisms. First, revenue from the opium trade could give field

commanders more flexibility to recruit and arm fighters. This would enable them to engage

in combat operations where the timing of attacks is less random and, therefore, easier for

state rivals to anticipate and engage in strategic adjustment. As such, battlefield losses are

likely. These losses are more easily absorbed if a given rebel division has more, better armed

combatants. Second, increasing capacity could make it easier for insurgents to deploy spies

or buy information about troop movement patterns from civilians. Responding strategically

to intelligence reports about time windows within which troops and bases are vulnerable

could lead to temporal clustering. Importantly, these are not rival mechanisms. They can

29

Table 5: Impact of rebel capacity on within-day randomization of indirect fire attacks,accounting for rebel intimidation tactics

Opium Revenue -0.0549∗∗∗ -0.0492∗∗∗ -0.0484∗∗∗

(0.0125) (0.0121) (0.0104)

Model ParametersFighting Season FE Yes Yes YesFS Trend Yes Yes YesPS Trend Yes Yes YesPLS Trend Yes Yes YesIntimidation YesCollaborator Killings YesModel StatisticsNo. of Observations 600 600 600No. of Clusters 154 154 154R2 0.187 0.204 0.227

Notes: Outcome of interest is the (log) p-value of the randomnesstest. The quantity of interest is opium revenue for a given district-year. All regressions include fighting season fixed effects as wellas controls for the intensive margin of fighting during the fighting,harvest, and planting seasons respectively. Additional parametersare noted in the table footer. Heteroskedasticity robust standarderrors clustered by district are reported in parentheses. Starsindicate *** p < 0.01, ** p < 0.05, * p < 0.1.

operate simultaneously.

Our data provides us with a unique opportunity to investigate the second mechanism more

precisely. In particular, we expect that conditions that make intelligence gathering easier

(i.e., reduced frictions) should enhance the negative effect of opium revenue on randomness

of combat. That is, in places where rebels have the ability to gather information about

troop and base vulnerabilities, temporal clustering should be even more responsive to rents

extracted from the opium trade.

We begin with the simplest test of this mechanism. We gather administrative data on

the distribution of ethnic groups across districts. We identify districts where 95% or more

of population settlements are classified as Pashto speaking. Pashtuns are Taliban coethnics

and form the primary base of civilian support for the insurgency. In principle, we expect

it will be easier for insurgents to acquire information about government activity in districts

30

dominated by their coethnics. We present these results in Table 6, Column 2. Notice that

the additive effect of opium revenue in coethnic zones is much larger (roughly 80%) than

non-coethnic districts. This is evidence consistent with our story, but relying on coethnicity

as a test of our argument may conflate intelligence frictions with a range of other factors as

well.

We overcome this concern by turning to more sophisticated tests of our argument. In

particular, our military records include previously unreleased information about rebel surveil-

lance of troop movement and base activity as well as data on security breaches, which occur

when insurgents are able to effectively infiltrate the outer perimeter of targets and observe

activity from within bases and outposts. These yield another potential test of our informa-

tion mechanism by tracking incidents where the Taliban are able to ‘turn’ security recruits

and use them to launch attacks from within army units. In each of these cases, we are

able to employ much more direct evidence of the ability of the insurgency to gather precise

information about target defenses. We test our mechanism using these data in Columns 3

through 5 in Table 6. In Column 3, we interact our measure of the spy network operations

with revenue.10 In Columns 4 and 5, we repeat this specification with measures of infiltration

and insider attacks. We find strong evidence that our main effect is enhanced in districts

where the insurgents have a demonstrated capability to conduct surveillance, infiltrate secu-

rity installations, and launch insider attacks. These findings yield evidence consistent with

the mechanism implied by our theoretical argument and suggest that intelligence gathering

may be a primary pathway through which shocks to rebel capacity influence the timing of

violent attacks.

10To avoid potential concerns about the endogeneity of intelligence gathering, we identify the cross sectionof districts with these characteristics using only the first year of our sample, 2006.

31

Table 6: Heterogeneous effects of rebel capacity on within-day randomization of indirect fireattacks with respect to potential intelligence gathering

Opium Revenue -0.0549∗∗∗ -0.0146∗ -0.0194∗∗∗ -0.0537∗∗∗ -0.0433∗∗∗

(0.0125) (0.00766) (0.00664) (0.0131) (0.00920)Coethnicity 0.378

(0.352)Coethnicity × Revenue -0.0552∗∗∗

(0.0168)Surveillance 0.953∗∗

(0.400)Surveillance × Revenue -0.0678∗∗∗

(0.0191)Infiltration 0.761∗∗

(0.307)Infiltration × Revenue -0.0308∗

(0.0161)Insiders -1.861

(1.511)Insiders × Revenue -0.0909∗∗∗

(0.0344)

Model ParametersFighting Season FE Yes Yes Yes Yes YesFS Trend Yes Yes Yes Yes YesPS Trend Yes Yes Yes Yes YesPLS Trend Yes Yes Yes Yes YesCoethnicity YesRebel Spies YesRebel Infiltration YesInsider Attacks YesModel StatisticsNo. of Observations 600 600 600 600 600No. of Clusters 154 154 154 154 154R2 0.187 0.218 0.233 0.188 0.278

Notes: Outcome of interest is the (log) p-value of the randomness test. The quantityof interest is opium revenue for a given district-year. All regressions include fightingseason fixed effects as well as controls for the intensive margin of fighting during thefighting, harvest, and planting seasons respectively. Additional parameters are notedin the table footer. Heteroskedasticity robust standard errors clustered by district arereported in parentheses. Stars indicate *** p < 0.01, ** p < 0.05, * p < 0.1.

32

5 Conclusion

Rebel tactics are an overlooked feature of internal warfare. Understanding how these con-

flicts are fought and the strategic responses of armed actors to revenue shocks is on equal

footing with thoroughly examined questions about the causes of civil war and the factors

that influence when hostilities end.

We argue that shocks to rebel capacity influence the timing of attacks. To clarify our ar-

gument, we develop a model of combat during an irregular insurgency. Rebels optimize when

they conduct attacks after observing imperfect signals of government defensive maneuvers.

As insurgents accumulate resources through taxation, their budget constraint is relaxed and

they can recruit more fighters, acquire more armaments, and gather more intelligence about

the vulnerability of troops and bases. The labor supply of fighters, coupled with surplus cap-

ital, allows rebels to conduct more attacks. Infiltrating military installations and conducting

surveillance of troop movement enhances the precision (quality) of information rebel leaders

have about specific times when attacks will yield the highest probability of success. Our

model implies revenue shocks will lead to clustering in the temporal distribution of violence.

Stated differently, the timing of attack patterns will increasingly deviate from randomness.

Our model also suggests that these tactical shifts will be greatest when armed actors have

the institutional capacity to pin-point when such attacks are least likely to be neutralized

by government defenses.

We test the empirical implications of our theoretical model using data collected during

Operational Enduring Freedom in Afghanistan. The temporal precision of our military

records enable us to develop a sophisticated methodology for differentiating the within-day

timing of rebel operations from randomized combat. This method produces a likelihood

parameter that quantifies the degree of temporal clustering present in the allocation of

insurgent attacks at the district level, broken down by fighting season. We couple this novel

33

approach with high resolution estimates of opium production and market prices. We leverage

the industrial organization of the Taliban, including their highly institutionalized taxation

system, to estimate the impact of local revenue from the drug trade on combat tactics in

the subsequent fighting season.

We find consistent evidence that positive shocks to rebel capacity decrease randomness

in the timing of violent attacks. Consistent with our model, indirect fire attacks (over which

rebels maintain unilateral control over timing) become concentrated during particular time

windows following opium tax windfalls. In other words, insurgents begin to concentrate

their combat operations during specific periods of the day. This finding survives a battery of

robustness checks, including accounting for trends in violence during the fighting, harvest,

and planting seasons. These results also hold when we introduce a number of alternative

measures of state capacity, including close air support missions, bomb neutralization, coun-

terinsurgent surveillance activity, and safe house raids. The incredibly rich nature of our

conflict microdata also allow us to rule out other potential identification concerns, including

rarely documented coercive tactics used by insurgents which may influence opium produc-

tion.

Our data also yields a unique opportunity to assess the mechanism suggested by our

model: intelligence gathering. Temporal clustering may occur because rebels use their re-

sources to improve the quality and precision of their information about target vulnerability.

This type of mechanism is largely unobserved and difficult to disentangle from alternative ex-

planations. Our military records, however, include detailed information about where rebels

were observed conducting surveillance operations as well as instances where insurgents were

able to infiltrate government installations and conduct insider attacks. The heterogeneous

effects we estimate produce evidence consistent with our theoretical model. The capacity

to gather intelligence substantially enhances the baseline effect of revenue shocks on combat

operations.

34

These findings reveal how rebel tactics are influenced by the ability to extract taxes from

the local population. As revenue increases, insurgents shift their combat operations in a

manner that prior theoretical accounts overlooked. The timing of their attacks becomes

less plausibly random and more easily predictable. This type of tactical shift could make it

easier for government forces to thwart rebel attacks. But our results suggest that positive

shocks to rebel capacity decrease the randomness of attacks the greatest under conditions

when rebels can acquire information about government defensive maneuvers, potentially

anticipate countermeasures, and calibrate the timing of their attacks accordingly.

Our results further unpack the political economy of conflict, with a focus on the industrial

organization of insurgency. Prior work provides compelling evidence that insurgents respond

strategically to local economic shocks (Dube and Vargas, 2013b; Berman et al., 2017; Oliver,

2018), form alliances during war (Konig et al., 2017), and calibrate their use of violence

against civilian populations (Condra and Shapiro, 2012; Condra et al., forthcoming). Our

evidence highlights how sophisticated institutions commonly associated with states and gov-

ernment forces—structured tax collection schemes, combat coordination, and surveillance

operations—influence the timing of insurgent violence.

35

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39

Table 7: Summary statistics

Variable Mean Std. Dev. Min. Max. NOutcome of InterestIndirect fire, likelihood parameter -7.025 3.918 -39.686 0 600Rebel CapacityOpium revenue 20.506 25.403 0 75.518 600Opium revenue, regional yield/prices 20.017 24.7 0 73.587 600Trends in ViolenceIndirect fire trend, fighting season 19.187 21.153 5 253 600Indirect fire trend, growing/harvest season 10.788 15.194 0 161 600Indirect fire trend, planting season 7.663 10.925 0 109 600

Notes: summary statistics are calculated for the sample studied in the main estimatingequation.

40

Theoretical Appendix

Proof of Proposition 1

For event S, the complement is denoted S ′.For each time slot, we say that H denotes the situation when protection is there, and

D signals that the time window is “defended”; a = P (D|H), b = P (V |H ′). Finally, let Cexplosion (attack is successful) during a period with an attack. We assume that P (C|H ′) = pand P (C|H) = 0.

The other parameters are: N is the number of time slots, G is the number of defensesallocated by the government, and A is the number of attacks.

A standard interpretation for a and b as a = P (positive test—disease) = sensitivity; andb = P (negative test—no disease)= specificity, two important characteristics of any statisticaltest.

Suppose that every time slot is protected with probability t; it is specified by distributionof G, G < N defenses among N time slots. Rebels have A attacks, test every time slot, andthus obtain a signal “defended” (D) or “vulnerable” (V ) in every time slot with probabilities

P (V ) = P (H)P (V |H) + P (H ′)P (V |H ′) = t(1− a) + (1− t)b,P (D) = P (H)P (D|H) + P (H ′)P (D|H ′) = ta+ (1− t)(1− b). (A1)

The optimal strategy for the government is to allocate G defenses uniformly over N timewindows. Then for each window t(G) = P (time slot is protected)= G

N.

We will show that for rebels the optimal strategy looks as follows. If A < x, the attacksare allocated uniformly at random among the vulnerable time slots. If A > x then there isthreshold value how many more put in the vulnerable time windows; then, they start to putinto the windows that tested “defended”, again uniformly.

First, observe that cases x = 0 and x = N are trivial: there is no information to infer, sothe optimal strategy for rebels is to allocate attacks uniformly across N time slots. In whatfollows, we will assume that 0 < x < N.

The total number of windows that are labeled vulnerable is N ≡ NN,G = N1 + N2,where N1 is number of slots that are vulnerable among the protected time slots and N2 inunprotected, i.e. Ni are independent binomial random variables with parameters (G, 1− a)and (N − G, b). Then EN = G(1 − a) + (N − G)b. We denote the event N(x) = (N = x),and the p.d.f. of N(x) as gN,G(x) = gN,G(x|a, b)), 0 ≤ x ≤ N . This p.d.f. can be calculatedby the standard discrete convolution formula

gN,G(x) =

min(x,G)∑i=0

p1(i)p2(x− i).

The critical ratio is defined by the following equation:

rN,G(x) = rN,G(x|a, b) =P (C|V N(x))

P (C|DN(x)).

A-1

Our aim is to establish that rN,G(x) ≥ 1.

Lemma A1 The following formulae are true for any x, 0 < x < N :

P (CV N(x)) =G

NpbgN−1,G(x− 1), (A2)

P (V N(x)) = gN,G(x)x

N, (A3)

P (CDN(x)) =G

Np(1− b)gN−1,G(x), (A4)

P (DN(x)) = gN,G(x)N − xN

. (A5)

Proof. First, observe that

P (V N(x)) = P (N(x))P (V |N(x)) = gN,G(x)x

N

as P (V |N(x)) = xN

, the probability for one slot to be labeled vulnerable among x to be in aparticular time window.

Similarly,

P (DN(x)) = P (N(x))P (D|N(x)) = gN,G(x)N − xN

.

Though events C and V (or D) are not independent, they are independent given H or H ′.Then, using total probability formula and P (C|H) = 0, we have

P (CV N(x)) = P (H)P (C|H)P (V N(x)|H) + P (H ′)P (C|H ′)P (V N(x)|H ′)= P (H ′)P (C|H ′)P (V N(x)|H ′).

Similarly,

P (CDN(x)) = P (H ′)P (C|H ′)P (DN(x)|H ′),P (V N(x)|H ′) = P (V |H ′)P (N(x)|V H ′),P (DN(x)|H ′) = P (D|H ′)P (N(x)|DH ′).

Now, we can show that

P (N(x))|H ′V ) = gN−1,G(x− 1),

P (N(x))|H ′D) = gN−1,G(x).

Indeed, if the total number of time slots marked “vulnerable” is x, and if a particular windowhas no defense, H ′, and is marked “vulnerable”, V , then in remaining N − 1 time slots thereare G defenses and x− 1 time slots that are marked vulnerable. If the total number of timeslots marked vulnerable is x, and a particular slot has no defense, H ′, and produced markD, then in remaining N − 1 windows there are G defended windows and x slots markedvulnerable. We also have P (H ′) = G

N, P (C|H ′) = p, P (V |H ′) = b, and P (D|H ′) = 1− b.

Now the following lemma that describes rN,G(x) is a straightforward corollary.

A-2

Lemma A2 The ratio is given by formula

rN,G(x) =P (C|V N(x))

P (C|DN(x))=

b

(1− b)(N − x)

x

gN−1,G(x− 1)

gN−1,G(x).

Lemma A3 Suppose that the signals are informative, i.e. a, b ≥ 1/2 and a + b > 1. Forany N,G, 0 < x < N, functions rN,G(x) > 1 and are monotonically increasing in x.

Proof. Let DN,G be a sum of N Bernoulli random variables, G have parameter 1− a, andN −G have parameter b > 1− a, 0 ≤ G ≤ N . Let

gN,G(x) = P (DN,G = x), 0 ≤ x ≤ N ;

fN,G(x) =gN,G(x− 1)

gN,G(x), 1 ≤ x ≤ N ;

rN,G(x) =N + 1− x

x

b

1− bfN,G(x), 1 ≤ x ≤ N.

We assume also that fN,G(0) = rN,G(0) = 0.Define c = b

1−ba

1−a , and observe that b+ a > 1 implies c > 1.It is easy to check that

rN,0(x) = 1, rN,N(x) = c, for 1 ≤ x ≤ N ;

rN,G(N) =Gc+N −G

N= 1 +

G

N(c− 1) for 0 ≤ G ≤ N .

(A6)

Using the total probability formula, we obtain a recursive relationship:

fN,G(x) =gN,G(x− 1)

gN,G(x)=

(1− b)gN−1,G(x− 1) + bgN−1,G(x− 2)

(1− b)gN−1,G(x) + bgN−1,G(x− 1)

=1− b+ bfN−1,G(x− 1)

1− bfN−1,G(x)

+ b

for 1 ≤ G, x ≤ N − 1 .(A7)

This implies that

rN,G(x) =N − x+ 1

x

b

1− b

1− b+ bx− 1

N − x+ 1

1− bb

rN−1,G(x− 1)

1− brN−1,G(x)

N − xx

1− bb

+ b

=N − x+ 1 + (x− 1)rN−1,G(x− 1)

N − xrN−1,G(x)

+ xfor 1 ≤ G, x ≤ N − 1 .

(A8)

A-3

Now, let us prove the following claim. For any N ≥ 1, 1 ≤ G ≤ N, x ≤ N, functionrN,G(x) as a function of a and b, depends only on c. When c grows from 1 to ∞, it is strictlyincreasing from 1.

The proof of the above claim follows from (A6) and induction by N , based on (A8).Indeed, (A6) implies that the induction statement holds for N = 1. By induction, thenumerator in (A8) is strictly increasing, and the denominator is strictly decreasing, andhence the right side in (A8) is strictly increasing and depends only on c.

Now we can show that for fixed N ≥ 2, 1 ≤ G ≤ N − 1, c > 1, function rN,G(x) isstrictly increasing in x.

Again, we use induction by N . Let r(x) = rN−1,G(x), H(x) = N − x + xr(x). Then, by(A8),

rN,G(x) = r(x)H(x− 1)

H(x), rN,G(x+ 1)− rN,G(x) =

C(x)

H(x+ 1)H(x),

where

C(x) = r(x+ 1)H2(x)− r(x)H(x+ 1)H(x− 1)

= r(x+ 1)[(N − x)2 + 2x(N − x)r(x) + x2r2(x)

]= −r(x)[N − x− 1 + (x+ 1)r(x+ 1)] [N − x+ 1 + (x− 1)r(x− 1)]

= r(x+ 1)[(N − x)2 + 2x(N − x)r(x) + x2r2(x)

].

We can check, using (A7) and (A8), that

r2,1(2) =1 + c

2> r2,1(1) =

2c

1 + c,

r3,1(3) =2 + c

3> r3,1(2) =

1 + 2c

2 + c> r3,1(1) =

3c

1 + 2c,

r3,2(3) =1 + 2c

3> r3,2(2) = c

2 + c

1 + 2c> r3,2(1) =

3c

2 + c,

and hence the proof is complete for N = 2 and N = 3.For N ≥ 4 and 2 ≤ x ≤ N − 2, we have x(N − x)−N ≥ 0, and hence by induction (??),

it follows that

C(x)>r(x)+r2(x)r(x+1)−r(x)r(x+1)− r2(x) = r(x)(r(x+ 1)− 1)(r(x)− 1) > 0

for 2 ≤ x ≤ N − 2.To prove the Lemma, it remains to show that rN−G,G(2)−rN−G,G(1) > 0 and rN−G,G(N)−

rN−G,G(N − 1) > 0. Using the total probability formula,

rN,G(N − 1) =2

N − 1

b

1− bP (DNG = N − 2)

P (DNG = N − 1)

=1

N − 1

(N −G)(N −G− 1) + 2(N −G)Gc+G(G− 1)c2

N −G+ cG.

(A9)

A-4

Then, using (A7), we obtain

rN,G(N)− rN,G(N − 1) =(N −G)G(c− 1)2

N(N − 1)(N −G+ cG)> 0 .

Similarly,

rN,G(2) =(N − 1)(c(N −G) +G)

c2(N −G)(N −G− 1) + 2(N −G)Gc+G(G− 1),

rN,G(1) =Nc

G+ c(1−G),

rN,G(2)− rN,G(1) =(N −G)G(c− 1)2

[c2(N −G)(N −G− 1) + 2(N −G)Gc+G(G− 1)](G+ c(1−G)).

Proof of Proposition 2

In our main setup a = b = θ > 12, which yields that

c(θ) =b

1− ba

1− a=

θ2

(1− θ)2> 1.

Also, c(θ) is strictly increasing in θ. Thus, Lemma applies: the critical ratio

rN,G(x) = rN,G(x|a = θ, b = θ))

is strictly increasing in θ. This in turns yields that the threshold a(x) that defines the optimalnumber of mortar attacks that should be allocated to vulnerable time slots is (weakly)increasing in θ, i.e. more attacks are concentrated on the vulnerable time slots. �

Proof of Proposition 3

(i) Let ϕ = ϕ(θ) be the probability of success for the rebels as a function of the precision ofinformation θ. Then ϕ (θ) − 1

2cIθ

2 satisfies the single-crossing property (in fact, increasingdifferences property) in (−cI , θ). Now, we can use Theorem 4 in Milgrom and Shannon(1994) to show that arg maxθ

{ϕ (θ)− 1

2cIθ

2}

is a monotone non-increasing function of cI .By Lemma A3, a fall in θ∗ implies that attacks become less concentrated as the marginalcost of information increases.

Similarly to (i), ϕ (θ) − 12cAA

2 satisfies the single-crossing property (in fact, increasingdifferences property) in (−cA, A), which implies that arg maxθ

{ϕ (θ)− 1

2cAA

2}

is a monotonenon-increasing function of cA.

(ii) Consider ϕ as a function of both θ and R, and observe that ϕ is increasing in θand decreasing in R, which implies that ϕ (θ, R) satisfies the single-crossing property in(−R, θ). (We ignored the cost terms, which are independent of R.) Again, Theorem 4 inMilgrom and Shannon (1994) shows that arg maxθ ϕ (θ, R) is monotone non-increasing in R.

A-5

By Lemma A3, a fall in θ∗ implies that attacks become less concentrated as the marginalcost of information increases.

Now, let us consider ϕ as a function of both θ and p, and observe that ϕ is increasingin both θ and p, which implies that ϕ (θ, p) satisfies the single-crossing property in (θ, p).(Again, ignoring the cost terms, which are independent of the success probability p.) This issufficient to conclude that arg maxθ ϕ (θ, p) is monotone non-decreasing in p, and use LemmaA3 to show that an increase in p leads to more concentrated attacks. �

A-6

Empirical Appendix

In this brief empirical appendix, we introduce supplemental analyses of close combat (directfire) and improvised explosive devices.

As we describe in the main text, insurgents have varying levels of control over the timingof their attacks. Indirect fire events can be initiated at any time against stationary targets likebases or military outposts. The timing of direct fire and IED attacks cannot be controlledunilaterally by rebels. Close combat, for example, is often characterized by attacks onconvoys and non-stationary targets. Troops and vehicles are rotated from locations on non-random schedules. The timing of these attacks, therefore, is consistently less random as aconsequence of government strategy, not rebel tactics. Similarly, IEDs may be emplacedhours or days before they are triggered by a passing convoy. Rank ordered, rebels have theleast control over the timing of roadside bomb attacks.

We replicate the visual evidence we introduce in our main results in Figures A-1 and A-2. Notice that direct fire, over which insurgents maintain some limited control over timing,is negatively correlated with revenue but the slope is consistently flatter than for indirectfire attacks (over which rebels have unilateral timing control). For IEDs, the coefficient iseffectively zero. We introduce the regression-based evidence in Tables A-1 and A-2. Althoughdirect fire attacks are consistently negatively correlated with revenue, the magnitude of themain effect (when compared to our indirect fire results) is consistently weaker. Similarly,although our point estimates are consistently negative with respect to roadside bombs, ourprecision is substantially diminished.

We interpret these findings as evidence consistent with our main results. A lack of controlover the timing attacks is analogous (statistically) to measurement error, which will lead toattenuation bias (towards zero).

A-7

Figure A-1: Bivariate relationship between opium revenue and p-value of randomization testof combat (direct fire attacks) in Afghanistan

0

20

40

60

80O

pium

reve

nue

-20 -15 -10 -5 0Logarithm of p-values from KS test -- Direct Fire Attacks

Observed opium revenue/p-value Fit line with 95% CI

Figure A-2: Bivariate relationship between opium revenue and p-value of randomization testof combat (IED attacks) in Afghanistan

-20

0

20

40

60

80

Opi

um re

venu

e

-15 -10 -5 0Logarithm of p-values from KS test -- IED Attacks

Observed opium revenue/p-value Fit line with 95% CI

A-8

Table A-1: Impact of rebel capacity on within-day randomization of direct fire attacks

Opium Revenue -0.0309∗∗∗ -0.0110∗∗∗ -0.0121∗∗∗ -0.0119∗∗∗

(0.00780) (0.00292) (0.00328) (0.00327)

Model ParametersFighting Season FE Yes Yes Yes YesFS Trend Yes Yes YesPS Trend Yes YesPLS Trend YesModel StatisticsNo. of Observations 1128 1128 1128 1128No. of Clusters 236 236 236 236R2 0.0963 0.448 0.450 0.464

Notes: Outcome of interest is the (log) p-value of the randomness test.The quantity of interest is opium revenue for a given district-year. All re-gressions include fighting season fixed effects. Column 2-4 add controls forthe intensive margin of fighting during the fighting, harvest, and plantingseasons respectively. Heteroskedasticity robust standard errors clusteredby district are reported in parentheses. Stars indicate *** p < 0.01, **p < 0.05, * p < 0.1.

A-9

Table A-2: Impact of rebel capacity on within-day randomization of IED attacks

Opium Revenue -0.00849∗∗ 0.000559 -0.000232 -0.00000219(0.00385) (0.00259) (0.00280) (0.00270)

Model ParametersFighting Season FE Yes Yes Yes YesFS Trend Yes Yes YesPS Trend Yes YesPLS Trend YesModel StatisticsNo. of Observations 653 653 653 653No. of Clusters 161 161 161 161R2 0.0700 0.179 0.186 0.186

Notes: Outcome of interest is the (log) p-value of the randomness test.The quantity of interest is opium revenue for a given district-year. All re-gressions include fighting season fixed effects. Column 2-4 add controls forthe intensive margin of fighting during the fighting, harvest, and plantingseasons respectively. Heteroskedasticity robust standard errors clusteredby district are reported in parentheses. Stars indicate *** p < 0.01, **p < 0.05, * p < 0.1.

A-10